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Block #402,843

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 2/13/2014, 5:26:41 PM Β· Difficulty 10.4376 Β· 6,393,468 confirmations

1CC
Cunningham Chain of the First Kind

A sequence where each prime is double the previous prime plus one.

Block Header
Block Hash
ece70d7c09f4505c8b63445a85c0d1501de7f9678da87f01c81aac7da2ec9734
View on Chainz β†—

Height

#402,843

Difficulty

10.437563

Transactions

1

Size

201 B

Version

2

Bits

0a700425

Nonce

121,662

Timestamp

2/13/2014, 5:26:41 PM

Confirmations

6,393,468

Merkle Root

e78e3beb5c5172e8acd50c848b87f313e76542c8b06a29d1ef04ed45227aa20d
Transactions (1)
Coinbasee78e3beb5c5172…04ed45227aa20d
1 in β†’ 1 out9.1600 XPM110 B
AeKNrjNj…1NEq95Ta
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.095 Γ— 10⁹⁢(97-digit number)
10952938419055649073…01873934886318423680
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

1
origin βˆ’ 1
1.095 Γ— 10⁹⁢(97-digit number)
10952938419055649073…01873934886318423679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.190 Γ— 10⁹⁢(97-digit number)
21905876838111298146…03747869772636847359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.381 Γ— 10⁹⁢(97-digit number)
43811753676222596293…07495739545273694719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.762 Γ— 10⁹⁢(97-digit number)
87623507352445192587…14991479090547389439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.752 Γ— 10⁹⁷(98-digit number)
17524701470489038517…29982958181094778879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.504 Γ— 10⁹⁷(98-digit number)
35049402940978077035…59965916362189557759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.009 Γ— 10⁹⁷(98-digit number)
70098805881956154070…19931832724379115519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.401 Γ— 10⁹⁸(99-digit number)
14019761176391230814…39863665448758231039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.803 Γ— 10⁹⁸(99-digit number)
28039522352782461628…79727330897516462079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.607 Γ— 10⁹⁸(99-digit number)
56079044705564923256…59454661795032924159
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Cunningham Chain of the First Kind. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

View full Prime Chain Discovery page β†’
β˜…β˜…β˜†β˜†β˜†
Rarity
UncommonChain length 10
How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Verify on a Primecoin Node

Anyone running a Primecoin node can independently verify this block using the following RPC commands. Run these from the primecoin-cli command line or via the debug console in the Primecoin wallet.

1. Get block hash by height
getblockhash 402843

Returns the block hash for a given block height. Use this to confirm the hash shown above matches the chain.

2. Get full block data
getblock ece70d7c09f4505c8b63445a85c0d1501de7f9678da87f01c81aac7da2ec9734

Returns the full block header including difficulty, prime chain origin, prime chain type, transaction IDs, and all other fields shown on this page.

How to run these commands: To verify this data independently, open a terminal on your own Primecoin node and run primecoin-cli <command>. Alternatively, open the Primecoin-Qt wallet, go to Help β†’ Debug Window β†’ Console, and type the command directly. The node must be fully synced to this block height for the commands to return results.

Cross-reference on Chainz Explorer

Chainz is an independent Primecoin block explorer. Compare this block's data to verify accuracy.

View Block #402,843 on Chainz β†—
Circulating Supply:57,614,475 XPMΒ·at block #6,796,310 Β· updates every 60s
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